We don't owe all the debt to ourselves. Each American's share right now is over $20,000, with a current national debt of about $5.7 trillion.
At the end of 1997 (latest data I could find), foreigners owned $1.8 trillion of U.S. debt, and chances are great it's much higher today, three years later. I'd guess (in round numbers) that foreigners own about half of the US debt.
The risk we have is that for whatever reason those other countries decide some day they don't want to be our bankers any more, and sell our bonds. The value of the dollar would drop, and things we buy from other countries would go up, causing inflation.